When the temperature of 4 moles of a gas was increased from `80^(@)C` to `100^(@)C`, at constant volume, the change in internal energy was 60J. What is the total heat capacity of the gas at constant volume ?

Options

A. 2 J/K
B. 4 J/K
C. 0.5 J/K
D. 3 J/K

Answer

D

Explanation

Heat required to increase the temperature at constant volume is
`Q_(V)=nC_(V)dT=4xxC_(V)xx(100-80)=80C_(V)`
But dQ = dU + dW, when the volume is kept constant
`W=PdV=0" "thereforedQ=dU`
`thereforeQ_(V)=80C_(V)=dU=60J" "thereforeC_(V)=60/80=0.75J//"mole"K`
`therefore` Heat capacity = `nC_(V)=4xx0.75=3J//K`